$\int x^{^{\frac23}}\,dx=$ $+C$
Explanation: The integrand is of the form $x^n$ where $n\neq-1$, so we can use the reverse power rule: $\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+C$ $\begin{aligned} \int x^{^{{\frac23}}}\,dx&=\dfrac{x^{^{{\frac23}+1}}}{{\dfrac23}+1}+C \\\\ &=\dfrac35x^{^{\frac53}}+C \end{aligned}$ In conclusion, $\int x^{^{\frac23}}\,dx=\dfrac35x^{^{\frac53}}+C$